My impression is the opposite to anyone receiving indulgent love "passively" - "amae" to me has always meant that those who do so actively expect to be forgiven for transgressions and be allowed to receive "love" (or be spoiled, essentially) from the person to whom they are ingratiating themselves. This isn't limited to children, and I don't actually think it's uniquely Japanese either. Amaenbou - ナ?テ??堋ヲ窶堙ア窶天ツ is how it's written - is one prone to this behaviour.